I'm just as curious of any opportunities. I know that there's Hollister Hills SVRA, but some parts are just too difficult for stock Subies.
I've scoured the bay area for off-roading places, and I did spot two trails (not sure if they're public or private) near Saratoga. I haven't actually driven them, and am very hesitant to enter them.
There's also two public dirt roads (not "real" off-roading, JUST dirt roads) I know of in Santa Clara County and San Benito County/Fresno County.
Summit Road eastbound towards Santa Cruz becomes a dirt road, then ends with a private road terminus. It starts at the southern end of California State Route 35 and ends in Santa Cruz (though not legally allowed, it is physically do-able). It is not well maintained and very narrow. In the daytime, local truck traffic is common, so it's not safe to pass through in the daytime.
Panoche Road in San Benito County and Fresno County is a well-maintained dirt road with two or three water crossings. One may use either California State Route 25 or Interstate 5 to get to it. It is wide enough most of the time for two vehicles to pass each other, and feels just like a gravel rally stage. I saw literally no traffic through it. Also, it's a wonderful scenic/fun route that connects Interstate 5 with US Route 101.